Strategies for two-player differential games with costly information

Abstract

In this work, a two players nonzero-sum differential game is considered, where one player tries to minimize some predefined cost and the other tries to maximize the same. The game is described by a stochastic differential system and the actions of the players serve as the control inputs to the dynamical system. The cost being a function of the actions chosen by the players and the state of the dynamical system, the players aim to control the state in order to optimize the cost functional. However in this problem the players do not have the access to the states for every time, rather the states are available at discrete time instances after some finite costs are paid by the players. The inclusion of the information-cost makes the structure of the cost functional non-classical. The work presents the strategies for the players under no-cost information access as well as under costly information access. Explicit time instances for the information access are also derived by solving certain finite dimensional optimization problems.